the best way to place crowds of animated objects
Maybe something like this?
All the particles are oriented towards the center of the emitter using Advanced Rotation settings for Hair particles:

I made a subdivided plane circular using a Simple Deform modifier.
Since the particles are emitted from the faces, I subdivided the faces in the back for a more even distribution.

I sloped the plane a bit and adjusted the rotation of the source objects of the particles accordingly and now it's like I'm in a stadium : )

EDIT:
It doesn't have to be Hairs; it can be Emitter.

I have no experience randomizing starting time of particle animations, though.

I'm not sure using Lifetime Randomness (which I assume you're referring to in your comment) can get the desired result.
I think you'd have to use something like this Animation Nodes add-onn
If you can do it without an add-on, I'd be interested to know how you do that. : )